Explain how you can find the decimal by thinking of the denominator as a 4 mental math

Answer 1

To find the decimal representation of a fraction with a denominator of 4 using mental math, you can think of the fraction in terms of quarters, since 4 is the number of quarters in a whole. Here’s how you can do it step by step:

1. Understanding the Fraction: Start with a fraction that has 4 as the denominator, such as $\frac{1}{4},\frac{2}{4},\frac{3}{4},\frac{4}{4}$, etc.

2. Convert to Quarters: Recognize that the denominator 4 means you're dividing something into 4 equal parts (quarters). For example:

   • $\frac{1}{4}$ means one quarter of a whole, which is 0.25.
   • $\frac{2}{4}$ means two quarters (or half of a whole), which is 0.50.
   • $\frac{3}{4}$ means three quarters, which is 0.75.
   • $\frac{4}{4}$ means four quarters, which equals 1.

3. General Rule: You can remember the following conversions:

   • $\frac{1}{4}=0.25$
   • $\frac{2}{4}=0.50$
   • $\frac{3}{4}=0.75$
   • $\frac{4}{4}=1.00$

4. Scaling Up: If you are working with larger numerators but still have 4 as the denominator, you can apply the same concept. For instance:

   • $\frac{5}{4}$: This is 1 quarter more than a whole (4/4), which is $1.00+0.25=1.25$.
   • $\frac{6}{4}$: This is $1.5$ (or $1\frac{2}{4}$), which is 1.50.
   • $\frac{7}{4}$: This equals $1.75$ (or $1\frac{3}{4}$).
   • $\frac{8}{4}$: This equals 2.00 (or just 2).

Using this method, you can mentally calculate the decimal representations of any fraction with a denominator of 4 by thinking in terms of quarters and adjusting for how many complete wholes you have.